A Novel SLM PAPR Reduction of OFDM Signals without Side ...
A Novel SLM PAPR Reduction of OFDM Signals without Side Information Toshiharu Kojima, Shohei Iwamoto, Yuki Shida, and Tadashi Fujino Department of Information and Communications Engineering, The University of Electro-Communications, Chofu, Tokyo, 182-8585, Japan Email: {kojimax, i-wamoto, shida, fujino}@ice.uec.ac.jp Telephone: +81-42-443-5763
Abstract—Selected mapping (SLM) is a well-known technique to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM). SLM generally requires the side information for each OFDM symbol, which leads to decrease the transmitting efficiency. In addition, false side information detection degrades the bit error rate (BER) performance significantly. In this paper, we propose a novel SLM scheme without any side information by devising a phase rotation and simple scrambler detection in the receiver. Computer simulation results show that the proposed scheme achieves excellent performances in terms of both PAPR reduction and BER.
II. C ONVENTIONAL S CHEME A. OFDM and PAPR An OFDM signal s(t) is represented as N −1 1 ∑ Xn ej2πn∆f t (0 ≤ t < Ts ) s(t) = √ N n=0
(1)
where N is the number of subcarriers, Ts is the duration of the OFDM symbol, and ∆f = 1/Ts is the subcarrier spacing. The PAPR of the OFDM signal is expressed as PAPR =
I. I NTRODUCTION
max0≤t≤Ts |s(t)|2 E[|s(t)|2 ]
(2)
B. Conventional Scheme Orthogonal frequency division multiplexing (OFDM) has been applied for various wireless applications due to high spectral efficiency and excellent anti-multipath fading capability. However, a large peak-to-average power ratio (PAPR) is a major disadvantage of OFDM, and thus various PAPR reduction techniques have been proposed for OFDM systems, such as clipping [1], block coding [2], partial transmit sequence (PTS) [3], and selected mapping (SLM) [4]. Among these methods, SLM has been well investigated because of its simple implementation and good PAPR reduction performance. In SLM, a transmitted data is input into multiple scramblers and apply a different phase rotation in each independent scrambler. After the IFFT, the OFDM symbol with the lowest PAPR is selected and transmitted. Side information which scrambler is selected must generally be transmitted for each symbol to recover the data, which leads to decrease the transmitting efficiency. Moreover, false side information detection causes the whole data symbol lost. Hence, it requires heavy forward error correction (FEC), which decreases the transmitting efficiency. To solve this problem, several techniques without sending side information have already been proposed such as [5]-[7]. In this paper, we propose a novel SLM scheme without side information by devising a phase rotation and simple scrambler detection in the receiver. The paper is organized as follows: In Section II, we briefly explain about OFDM and PAPR, and a conventional scheme. In Section III, the proposed SLM model is presented. In Section IV, we present simulation results for the proposed scheme. Finally, we summarize and conclude the paper in Section V.
978-1-4244-9991-5/11/$26.00 ©2011 IEEE
Fig. 1 shows the conventional SLM scheme. In Fig. 1, transmitted data is input to the mapper and a transmitted symbol X = [X0 , X1 , · · · , XN −1 ] is generated in the mapper. Then the transmitted symbol X is input to U scramblers. In each scrambler, the transmitted symbol X is scrambled, resulting in a following scrambled symbol X u :
where
X u = XP u
(3)
[ ] P u = diag pu0 , pu1 , · · · , puN −1
(4)
is a scramble matrix and pun ∈ {±1, ±j}
(u = 0, 1, · · · , N − 1)
(5)
u
Each scrambled symbol X is modulated into an OFDM symbol xu in the OFDM modulator. Then the OFDM symbol with the lowest PAPR among all xu is selected and transmitted. If the symbol xm is transmitted, the selected number m is also transmitted as a side information. In this scheme, log2 U bits are required for the side information to recover the data in the receiver. This causes a decrease of transmission efficiency. In the receiver, the OFDM demodulation is performed first. ˆ is descrambled based on a received A demodulated symbol X side information m, ˆ resulting in a received symbol Y : ˆ ˆ m∗ Y = XP
(6)
After the data decision, a received data is finally output. In the conventional scheme, if the received side information m ˆ is incorrect, the demodulated symbol Y is incorrectly descrambled. This causes a significant BER degradation.
321
Fig. 1.
Conventional SLM with side information
Fig. 2.
Proposed SLM Model
III. P ROPOSED S CHEME Fig. 2 shows the proposed scheme. In the transmitter, transmitted data is input to the signal mapper and a transmitted symbol X = [X0 , X1 , · · · , XN −1 ] is generated. Then the transmitted symbol X is input to U scramblers simultaneously. In the u-th (U = 0, 1, · · · , U − 1) scrambler, the transmitted symbol X is scrambled, resulting in a following scrambled symbol X u :
where
X u = XQu
(7)
] [ u u u Qu = diag ejφq0 , ejφq1 , · · · , ejφqN −1
(8)
is the u-th scramble matrix, φ ∈ [0, 2π) is a rotation phase, and qiu ∈ {0, 1}. The rotation phase φ is decided according to the primary modulation (signal mapping). Hereafter, the sequence {qnu } is called the u-th scrambler sequence. In the OFDM modulators, each scrambled symbol X u is modulated into U OFDM symbols xu . Then, the OFDM symbol with the lowest PAPR among all xu is selected for transmission. In the receiver, the OFDM demodulation is performed first. ˆ is input to U descramblers Then a demodulated symbol X
978-1-4244-9991-5/11/$26.00 ©2011 IEEE
simultaneously. In the u-th U = 0, 1, · · · , U − 1 descrambler, ˆ is descrambled, resulting in the the demodulated symbol X following u-th candidate symbol Y u : ˆ u∗ Y u = XP
(9)
After descrambling, by calculating an evaluation function depending on the phase rotation, we can estimate which scrambled symbol is selected and transmitted in the transmitter. Let θiu denote a phase of the subcarrier of the u-th candidate symbol Y u . In the case of quaternary phase-shift keying (QPSK) mapping, the evaluation function J(u) is defined by J(u) =
N −1 ( ∑ i=0
π) ( π ) u − φmod θi mod 2 2
(10)
Fig. 3 (a)-(d) shows an example for calculating J(u). The received signal phase is assumed to be θiu as shown in Fig. 3 (a). First, in Fig. 3 (b), the received signal phase θiu is normalized into a first quadrant by performing (θiu modπ/2). Next, the phase difference from a correct signal is calculated by subtracting (φmodπ/2) shown in Fig. 3 (c) and its absolute value shown in Fig. 3 (d) expresses an absolute phase error.
322
(a) Received Signal!
(b) Normalization!
Prob. of False Scrambler Detection Pf
1
Received Signal
N = 64 Eb /N0 = 1.0[dB] 0.8
0.6
0.4
0.2
0
-/ −π
-3//4 −π/2 -//2 −3π/4
Fig. 4.
-//4 −π/4
0
//4 π/4
//2 π/2
3//4 3π/4
π/
φq
Rotation phase dependence of Pf
(d) Absolute phase error !
(c) Offset!
Fig. 3.
Example of the evaluation function J(n) TABLE I S IMULATION C ONDITIONS
Modulation (mapping)
QPSK
Number of subcarriers N
64, 128, 512, 1024
Scramble sequence qiu
M sequence
Oversampling factor
4
Channel model
AWGN
Thus, the evaluation function J(u) expresses the total absolute phase error from the correct mapping. In other words, the evaluation function J(u) is the phase likelihood. Therefore, it is expected that the evaluation function takes a minimum value when the candidate symbol is correctly descrambled. That is, by selecting the candidate symbol with the smallest evaluation function, we can estimate the transmitted scrambled symbol without any side information. What is more, the evaluation function can realize only adder and subtracter, resulting in a simple implementation. After the data decision, a received data is finally output. IV. C OMPUTER S IMULATION In this section, we evaluate the performance of the proposed SLM scheme for QPSK mapping under the condition shown in Table I. A. Optimal rotation phase We define a ‘false scrambler detection’ as the case that J(m) does not take the minimum value in the receiver though the OFDM symbol xm is selected in the transmitter. If the false scrambler detection occurs, the incorrect descrambled symbol is output and the BER performance is degraded. Both a probability of the false scrambler detection Pf and the performance of the PAPR reduction depend on the rotation phase φ. In the following, we decide an optimal rotation phase φopt in the sense of minimizing Pf and maximizing the PAPR
978-1-4244-9991-5/11/$26.00 ©2011 IEEE
Fig. 5.
Rotation phase dependence of CCDF
reduction performance. First, Fig. 4 shows a rotation phase dependence of Pf , for φ ∈ [−π, π]. The system parameters are: N = 64, Eb /N0 = 1.0[dB], AWGN channel, and QPSK mapping. As can be seen from Fig. 4, the probability of the false scrambler detection depends on the phase rotation φ and takes the minimum one when φ equals to ±π/4, ±3π/4. Next, Fig. 5 shows a rotation phase dependence of a complementary cumulative distribution function (CCDF) of PAPR for N = 1024 and U = 4 with the phase rotation φ = 0, π/4, π/2, 3π/4, π. As can be seen from Fig. 5, a good PAPR performance is obtained when |φ| ≥ 3π/4. From these results, we conclude that φopt = ±3π/4 for the QPSK mapping. B. PAPR reduction performance Hereafter, we fix the rotation phase φ at its optimal value 3π/4. Fig. 6 shows the CCDF of PAPR for N = 1024 with U = 1, 2, · · · , 5. As can be seen from Fig. 6, the PAPR reduction performance of the proposed scheme is identical with that of the conventional scheme.
323
false scrambler detection ratio
10-2 10-3 -4
10-5 10-6
0.5
1 Eb/N0 [dB]
1.5
2
Probability of the false scrambler detection Pf
100
3
Proposed Scheme Ideal Linear
10-1
Linear
2 1
10-2
p =3
p = 30
0
BER
Output Power [dB]
0
Fig. 8.
CCDF of PAPR
4
p =2
-1
10-3 10-4
-2
N = 1024 U =4 OBO = 1dB
10-5
-3 -4 -5
N = 1024 U =4
10
10-7
Fig. 6.
OBO=1[dB] OBO=2[dB] OBO=3[dB] OBO=4[dB] OBO=5[dB] OBO=6[dB]
10-6 -5
-4
-3
Fig. 7.
-2
-1 0 Input Power [dB]
1
2
3
Nonlinear characteristics
C. False scrambler detection probability and BER performance In this subsection, we consider a nonlinear characteristics of amplifier using Rapp’s model [8]. It is represented as ρ F [ρ] = (11) 1 ρ 2p 2p {1 + ( B ) } where ρ is the amplitude of input signal, B is the output saturated level, p is a smoothness parameter. Fig. 7 shows inputoutput characteristics with B = 0 [dB]. In our simulations, we use with p = 3 that gives a good approximation of nonlinear amplifier. Fig. 8 shows the probability of the false scrambler detection Pf with output back-off (OBO) = 1, 2, · · · , 6 dB and U = 4. As can be seen from Fig. 8, Pf degrades when OBO decreases. Therefore we evaluate the influence of Pf on BER at OBO = 1 dB as the worst case. Fig. 9 shows the BER performance at OBO = 1 dB. In the figure, ’Ideal’ means the BER performance without false scrambler detection (i.e. selected scrambler is known). Fig. 9
978-1-4244-9991-5/11/$26.00 ©2011 IEEE
0
1
4
Fig. 9.
2
3
4
5 6 Eb/N0 [dB]
7
8
9
10
BER performance of the proposed scheme
shows that the false scrambler detection does not influence on the BER performance of the proposed scheme. V. C ONCLUSION In this paper, we propose the novel SLM scheme without sending explicit side information. The proposed scheme defines the arbitrary phase rotation according to the primary modulation in the scrambler and the evaluation function corresponding to the phase rotation in the receiver. The evaluation function that enables to detect the scrambler can realize only adder and subtracter, resulting in a simple implementation. Finally, results of the computer simulation show that the proposed scheme achieves an excellent performance in terms of both BER and PAPR reduction. R EFERENCES [1] X. Li and L. J. Cimini, Jr., “Effects of clipping and filtering on the performance of OFDM,” in IEEE Commun. Lett., vol. 2, no. 5, pp. 131133, May 1998.
324
[2] A. E. Jones, T. A. Wilkinson, and S. K. Barton,“Block coding scheme for reduction of peak to mean envelope power ratio of multicarrier transmission schemes,” Electron. Lett., vol. 30, no. 25, pp. 2098-2099, Dec. 1994. [3] S. H. M¨uller and J. B. H¨uber, “OFDM with reduced peak-to-average power ratio by optimum combination of partial transmit sequences,” Electron. Lett., vol. 33, no. 5, pp. 368-369, Feb 1997. [4] R. W. B¨auml, R. F. H. Fischer, and J. B. Huber, “Reducing the peakto-average power ratio of multicarrier modulation by selected mapping,” Electron. Lett., vol. 32, no. 22, pp. 2056-2057, Oct. 1996. [5] M. Breiling, S. H. M¨uller-Weinfurtner, and J. B. Huber, “Distortionless reduction of peak power without explicit side information,” in Proc. IEEE GLOBECOM ’00, vol. 3, pp. 1494-1498, Nov. 2000. [6] A. D. S. Jayalath and C. Tellambura, “SLM and PTS peak-power reduction without explicit side information,” IEEE Trans. Wireless Commun., vol.4, no.5, pp.2016-2013, Sept. 2005. [7] S. Y. L. Goff, S. S. Al-Samahi, B. K. Khoo, C. C. Tsimenidis, and B. S. Sharif, “Selected mapping without side information for PAPR reduction in OFDM,” IEEE Trans. Wireless Commun., vol. 8, no. 7, pp. 3320-3325, July 2009. [8] C. Rapp, “Effects of HPA-nonlinearity on 4-DPSK/OFDM signal for a digital sound broadcasting system,” 2nd European Conference on Satellite Commun., pp. 179-184, Oct 1991.
978-1-4244-9991-5/11/$26.00 ©2011 IEEE
325
Abstract—Selected mapping (SLM) is a well-known technique to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM). SLM generally requires the side information for each OFDM symbol, which leads to decrease the transmitting efficiency. In addition, false side information detection degrades the bit error rate (BER) performance significantly. In this paper, we propose a novel SLM scheme without any side information by devising a phase rotation and simple scrambler detection in the receiver. Computer simulation results show that the proposed scheme achieves excellent performances in terms of both PAPR reduction and BER.
II. C ONVENTIONAL S CHEME A. OFDM and PAPR An OFDM signal s(t) is represented as N −1 1 ∑ Xn ej2πn∆f t (0 ≤ t < Ts ) s(t) = √ N n=0
(1)
where N is the number of subcarriers, Ts is the duration of the OFDM symbol, and ∆f = 1/Ts is the subcarrier spacing. The PAPR of the OFDM signal is expressed as PAPR =
I. I NTRODUCTION
max0≤t≤Ts |s(t)|2 E[|s(t)|2 ]
(2)
B. Conventional Scheme Orthogonal frequency division multiplexing (OFDM) has been applied for various wireless applications due to high spectral efficiency and excellent anti-multipath fading capability. However, a large peak-to-average power ratio (PAPR) is a major disadvantage of OFDM, and thus various PAPR reduction techniques have been proposed for OFDM systems, such as clipping [1], block coding [2], partial transmit sequence (PTS) [3], and selected mapping (SLM) [4]. Among these methods, SLM has been well investigated because of its simple implementation and good PAPR reduction performance. In SLM, a transmitted data is input into multiple scramblers and apply a different phase rotation in each independent scrambler. After the IFFT, the OFDM symbol with the lowest PAPR is selected and transmitted. Side information which scrambler is selected must generally be transmitted for each symbol to recover the data, which leads to decrease the transmitting efficiency. Moreover, false side information detection causes the whole data symbol lost. Hence, it requires heavy forward error correction (FEC), which decreases the transmitting efficiency. To solve this problem, several techniques without sending side information have already been proposed such as [5]-[7]. In this paper, we propose a novel SLM scheme without side information by devising a phase rotation and simple scrambler detection in the receiver. The paper is organized as follows: In Section II, we briefly explain about OFDM and PAPR, and a conventional scheme. In Section III, the proposed SLM model is presented. In Section IV, we present simulation results for the proposed scheme. Finally, we summarize and conclude the paper in Section V.
978-1-4244-9991-5/11/$26.00 ©2011 IEEE
Fig. 1 shows the conventional SLM scheme. In Fig. 1, transmitted data is input to the mapper and a transmitted symbol X = [X0 , X1 , · · · , XN −1 ] is generated in the mapper. Then the transmitted symbol X is input to U scramblers. In each scrambler, the transmitted symbol X is scrambled, resulting in a following scrambled symbol X u :
where
X u = XP u
(3)
[ ] P u = diag pu0 , pu1 , · · · , puN −1
(4)
is a scramble matrix and pun ∈ {±1, ±j}
(u = 0, 1, · · · , N − 1)
(5)
u
Each scrambled symbol X is modulated into an OFDM symbol xu in the OFDM modulator. Then the OFDM symbol with the lowest PAPR among all xu is selected and transmitted. If the symbol xm is transmitted, the selected number m is also transmitted as a side information. In this scheme, log2 U bits are required for the side information to recover the data in the receiver. This causes a decrease of transmission efficiency. In the receiver, the OFDM demodulation is performed first. ˆ is descrambled based on a received A demodulated symbol X side information m, ˆ resulting in a received symbol Y : ˆ ˆ m∗ Y = XP
(6)
After the data decision, a received data is finally output. In the conventional scheme, if the received side information m ˆ is incorrect, the demodulated symbol Y is incorrectly descrambled. This causes a significant BER degradation.
321
Fig. 1.
Conventional SLM with side information
Fig. 2.
Proposed SLM Model
III. P ROPOSED S CHEME Fig. 2 shows the proposed scheme. In the transmitter, transmitted data is input to the signal mapper and a transmitted symbol X = [X0 , X1 , · · · , XN −1 ] is generated. Then the transmitted symbol X is input to U scramblers simultaneously. In the u-th (U = 0, 1, · · · , U − 1) scrambler, the transmitted symbol X is scrambled, resulting in a following scrambled symbol X u :
where
X u = XQu
(7)
] [ u u u Qu = diag ejφq0 , ejφq1 , · · · , ejφqN −1
(8)
is the u-th scramble matrix, φ ∈ [0, 2π) is a rotation phase, and qiu ∈ {0, 1}. The rotation phase φ is decided according to the primary modulation (signal mapping). Hereafter, the sequence {qnu } is called the u-th scrambler sequence. In the OFDM modulators, each scrambled symbol X u is modulated into U OFDM symbols xu . Then, the OFDM symbol with the lowest PAPR among all xu is selected for transmission. In the receiver, the OFDM demodulation is performed first. ˆ is input to U descramblers Then a demodulated symbol X
978-1-4244-9991-5/11/$26.00 ©2011 IEEE
simultaneously. In the u-th U = 0, 1, · · · , U − 1 descrambler, ˆ is descrambled, resulting in the the demodulated symbol X following u-th candidate symbol Y u : ˆ u∗ Y u = XP
(9)
After descrambling, by calculating an evaluation function depending on the phase rotation, we can estimate which scrambled symbol is selected and transmitted in the transmitter. Let θiu denote a phase of the subcarrier of the u-th candidate symbol Y u . In the case of quaternary phase-shift keying (QPSK) mapping, the evaluation function J(u) is defined by J(u) =
N −1 ( ∑ i=0
π) ( π ) u − φmod θi mod 2 2
(10)
Fig. 3 (a)-(d) shows an example for calculating J(u). The received signal phase is assumed to be θiu as shown in Fig. 3 (a). First, in Fig. 3 (b), the received signal phase θiu is normalized into a first quadrant by performing (θiu modπ/2). Next, the phase difference from a correct signal is calculated by subtracting (φmodπ/2) shown in Fig. 3 (c) and its absolute value shown in Fig. 3 (d) expresses an absolute phase error.
322
(a) Received Signal!
(b) Normalization!
Prob. of False Scrambler Detection Pf
1
Received Signal
N = 64 Eb /N0 = 1.0[dB] 0.8
0.6
0.4
0.2
0
-/ −π
-3//4 −π/2 -//2 −3π/4
Fig. 4.
-//4 −π/4
0
//4 π/4
//2 π/2
3//4 3π/4
π/
φq
Rotation phase dependence of Pf
(d) Absolute phase error !
(c) Offset!
Fig. 3.
Example of the evaluation function J(n) TABLE I S IMULATION C ONDITIONS
Modulation (mapping)
QPSK
Number of subcarriers N
64, 128, 512, 1024
Scramble sequence qiu
M sequence
Oversampling factor
4
Channel model
AWGN
Thus, the evaluation function J(u) expresses the total absolute phase error from the correct mapping. In other words, the evaluation function J(u) is the phase likelihood. Therefore, it is expected that the evaluation function takes a minimum value when the candidate symbol is correctly descrambled. That is, by selecting the candidate symbol with the smallest evaluation function, we can estimate the transmitted scrambled symbol without any side information. What is more, the evaluation function can realize only adder and subtracter, resulting in a simple implementation. After the data decision, a received data is finally output. IV. C OMPUTER S IMULATION In this section, we evaluate the performance of the proposed SLM scheme for QPSK mapping under the condition shown in Table I. A. Optimal rotation phase We define a ‘false scrambler detection’ as the case that J(m) does not take the minimum value in the receiver though the OFDM symbol xm is selected in the transmitter. If the false scrambler detection occurs, the incorrect descrambled symbol is output and the BER performance is degraded. Both a probability of the false scrambler detection Pf and the performance of the PAPR reduction depend on the rotation phase φ. In the following, we decide an optimal rotation phase φopt in the sense of minimizing Pf and maximizing the PAPR
978-1-4244-9991-5/11/$26.00 ©2011 IEEE
Fig. 5.
Rotation phase dependence of CCDF
reduction performance. First, Fig. 4 shows a rotation phase dependence of Pf , for φ ∈ [−π, π]. The system parameters are: N = 64, Eb /N0 = 1.0[dB], AWGN channel, and QPSK mapping. As can be seen from Fig. 4, the probability of the false scrambler detection depends on the phase rotation φ and takes the minimum one when φ equals to ±π/4, ±3π/4. Next, Fig. 5 shows a rotation phase dependence of a complementary cumulative distribution function (CCDF) of PAPR for N = 1024 and U = 4 with the phase rotation φ = 0, π/4, π/2, 3π/4, π. As can be seen from Fig. 5, a good PAPR performance is obtained when |φ| ≥ 3π/4. From these results, we conclude that φopt = ±3π/4 for the QPSK mapping. B. PAPR reduction performance Hereafter, we fix the rotation phase φ at its optimal value 3π/4. Fig. 6 shows the CCDF of PAPR for N = 1024 with U = 1, 2, · · · , 5. As can be seen from Fig. 6, the PAPR reduction performance of the proposed scheme is identical with that of the conventional scheme.
323
false scrambler detection ratio
10-2 10-3 -4
10-5 10-6
0.5
1 Eb/N0 [dB]
1.5
2
Probability of the false scrambler detection Pf
100
3
Proposed Scheme Ideal Linear
10-1
Linear
2 1
10-2
p =3
p = 30
0
BER
Output Power [dB]
0
Fig. 8.
CCDF of PAPR
4
p =2
-1
10-3 10-4
-2
N = 1024 U =4 OBO = 1dB
10-5
-3 -4 -5
N = 1024 U =4
10
10-7
Fig. 6.
OBO=1[dB] OBO=2[dB] OBO=3[dB] OBO=4[dB] OBO=5[dB] OBO=6[dB]
10-6 -5
-4
-3
Fig. 7.
-2
-1 0 Input Power [dB]
1
2
3
Nonlinear characteristics
C. False scrambler detection probability and BER performance In this subsection, we consider a nonlinear characteristics of amplifier using Rapp’s model [8]. It is represented as ρ F [ρ] = (11) 1 ρ 2p 2p {1 + ( B ) } where ρ is the amplitude of input signal, B is the output saturated level, p is a smoothness parameter. Fig. 7 shows inputoutput characteristics with B = 0 [dB]. In our simulations, we use with p = 3 that gives a good approximation of nonlinear amplifier. Fig. 8 shows the probability of the false scrambler detection Pf with output back-off (OBO) = 1, 2, · · · , 6 dB and U = 4. As can be seen from Fig. 8, Pf degrades when OBO decreases. Therefore we evaluate the influence of Pf on BER at OBO = 1 dB as the worst case. Fig. 9 shows the BER performance at OBO = 1 dB. In the figure, ’Ideal’ means the BER performance without false scrambler detection (i.e. selected scrambler is known). Fig. 9
978-1-4244-9991-5/11/$26.00 ©2011 IEEE
0
1
4
Fig. 9.
2
3
4
5 6 Eb/N0 [dB]
7
8
9
10
BER performance of the proposed scheme
shows that the false scrambler detection does not influence on the BER performance of the proposed scheme. V. C ONCLUSION In this paper, we propose the novel SLM scheme without sending explicit side information. The proposed scheme defines the arbitrary phase rotation according to the primary modulation in the scrambler and the evaluation function corresponding to the phase rotation in the receiver. The evaluation function that enables to detect the scrambler can realize only adder and subtracter, resulting in a simple implementation. Finally, results of the computer simulation show that the proposed scheme achieves an excellent performance in terms of both BER and PAPR reduction. R EFERENCES [1] X. Li and L. J. Cimini, Jr., “Effects of clipping and filtering on the performance of OFDM,” in IEEE Commun. Lett., vol. 2, no. 5, pp. 131133, May 1998.
324
[2] A. E. Jones, T. A. Wilkinson, and S. K. Barton,“Block coding scheme for reduction of peak to mean envelope power ratio of multicarrier transmission schemes,” Electron. Lett., vol. 30, no. 25, pp. 2098-2099, Dec. 1994. [3] S. H. M¨uller and J. B. H¨uber, “OFDM with reduced peak-to-average power ratio by optimum combination of partial transmit sequences,” Electron. Lett., vol. 33, no. 5, pp. 368-369, Feb 1997. [4] R. W. B¨auml, R. F. H. Fischer, and J. B. Huber, “Reducing the peakto-average power ratio of multicarrier modulation by selected mapping,” Electron. Lett., vol. 32, no. 22, pp. 2056-2057, Oct. 1996. [5] M. Breiling, S. H. M¨uller-Weinfurtner, and J. B. Huber, “Distortionless reduction of peak power without explicit side information,” in Proc. IEEE GLOBECOM ’00, vol. 3, pp. 1494-1498, Nov. 2000. [6] A. D. S. Jayalath and C. Tellambura, “SLM and PTS peak-power reduction without explicit side information,” IEEE Trans. Wireless Commun., vol.4, no.5, pp.2016-2013, Sept. 2005. [7] S. Y. L. Goff, S. S. Al-Samahi, B. K. Khoo, C. C. Tsimenidis, and B. S. Sharif, “Selected mapping without side information for PAPR reduction in OFDM,” IEEE Trans. Wireless Commun., vol. 8, no. 7, pp. 3320-3325, July 2009. [8] C. Rapp, “Effects of HPA-nonlinearity on 4-DPSK/OFDM signal for a digital sound broadcasting system,” 2nd European Conference on Satellite Commun., pp. 179-184, Oct 1991.
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325
